Optimal Stopping with Trees: The Details

Abstract

The purpose of this paper is two-fold, first, to review a recent method introduced by S. Becker, P. Cheridito, and P. Jentzen, for solving high-dimensional optimal stopping problems using deep Neural Networks, second, to propose an alternative algorithm replacing Neural Networks by CART-trees which allow for more interpretation of the estimated stopping rules. We in particular compare the performance of the two algorithms with respect to the Bermudan max-call benchmark example concluding that the Bermudan max-call may not be suitable to serve as a benchmark example for high-dimensional optimal stopping problems. We also show how our algorithm can be used to plot stopping boundaries.